Number theory

This free course is an introduction to Number Theory. Section 1 provides a brief introduction to the kinds of problem that arise in Number Theory. Section 2 reviews and provides a more formal approach to a powerful method of proof, mathematical induction. Section 3 introduces and makes precise the key notion of divisibility. The Division Algorithm, concerning the division of one integer by another, is used. Its consequences, both practical and theoretical, make it a cornerstone of number theory. Section 4 explores some of the basic properties of the prime numbers and introduces the sieve of Eratosthenes.

Course learning outcomes

After studying this course, you should be able to:

Use, and understand the theoretical underpinnings of, mathematical induction

Understand and be able to apply the Generalised Principle of Mathematical Induction and the Second Principle of Mathematical Induction

Recognise the importance of the Division Algorithm, and be able to apply it in a variety of scenarios

Understand the term ‘prime number’, and be able to recall basic properties of integers relating to prime numbers

Find all prime numbers in a given range using the sieve of Eratosthenes.